The generator matrix

 1  0  0  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1 3X  1 3X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  1  2  4 3X 3X+4  1 3X+2  1 3X  3  2 3X+2  0 2X+3 3X+4 2X+4 4X+3 3X+3 X+3  4  X 3X+1  1 X+4  1  1 X+3 2X X+1  0 3X+3  3 2X+4 3X+4 2X+3 3X+1 X+2 3X+3 2X+1 3X+2 3X+1
 0  0  1  3  2  1 3X+4 3X+3  1 3X+4  3 3X+1 2X  0 X+3 3X+2  3 X+2 2X X+4 2X+1 4X+2 2X+4 X+3 X+4 3X+2 3X+1 X+1 2X+4 2X+4  3 3X+3  1 X+1 X+4 2X+2 3X+3 2X+2 3X+2 2X+4 2X+4 3X+2 X+2 3X+3
 0  0  0 3X 4X  0  X 4X  X 3X 4X 2X 2X  X 2X 2X  0 3X 4X  0  X 2X  X 4X 2X 2X 3X 3X 3X 3X  X 2X 4X 3X 4X  0  X 4X 3X  X 2X  0 3X 4X

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+480x^161+480x^162+400x^163+1000x^164+1228x^165+2680x^166+2340x^167+1140x^168+2160x^169+1892x^170+4880x^171+3660x^172+2580x^173+4320x^174+2780x^175+7480x^176+5680x^177+3820x^178+4880x^179+3176x^180+7280x^181+4400x^182+2060x^183+2640x^184+1460x^185+2200x^186+940x^187+32x^190+16x^195+12x^200+12x^205+8x^210+8x^215

The gray image is a linear code over GF(5) with n=220, k=7 and d=161.
This code was found by Heurico 1.16 in 66.4 seconds.